The corps commanders of the Army of the Potomac, in 1862, concluded that about 40,000 men (PFD, split between the Washington Defences themselves and a covering force) would suffice to defend the capital and the rest would be available for offensive operations.
1862, Peninsular Campaign: McClellan plans to leave something over 50,000 men defending the capital and in the covering force. Lincoln intervenes to up the total men defending the capital and in the covering force to greater than the strength of McClellan's field army; troops get slowly released, but at the crisis point of the Peninsular Campaign in the Seven Days there are over 70,000 men around Washington and in the covering force (amalgamated as Pope's Army of Virginia by that point) and McClellan is forced away from Richmond for want of ~20,000 men to cover his exposed right flank. Those troops had been promised to be sent to him for more than a month.
(He never gets them.)
1862, Antietam: The force defending Washington during the Maryland Campaign is slightly harder to determine, but here:
Forces McClellan brought back from the Peninsula: 81,700 (August 10 strength)
AoV plus defences of Washington, June 30: ~70,000, of which ~5,000 were en route to the Army of the Potomac on that date. (This does not include the Middle Department.) This is 65,000 PFD as the other 5,000 are embraced in the AotP strength.
Reinforcements with Burnside (from his department and another): ~13,500 PFD.
Subsequent new recruits:
This is the hardest one to estimate, but Humphreys (7,000 PFD, 8 regiments) implies ca. 800 PFD per brand new regiment. Sticking with just the inf regiments for now and counting only new arrivals, not those shuffled about:
The Middle Department acquired eleven new regiments (as in, regiments that joined from their state) in August and September.
The Mil Dist of Washington gained eight in August for Defences North of the Potomac, seven in Unassigned Infantry, and seventeen in Whipple's division.
In September, Whipple's division gained one, Casey's provisional brigade gained one, the Defences North of the Potomac gained one and the Unassigned Infantry gained five (though that last group all arrived right at the end of the month so can be ignored). This doesn't count all the temporary militia showing up.
These categories mostly do not overlap with Humphreys Division (though two regiments do)
This means that over the course of August and September the influx of reinforcement regiments exclusive of Humphreys is 11+8+7+17+1+1+1-2, for 44. That amounts to about 35,000 PFD.
Humphreys is 7,000 PFD.
Total before casualties: 42,000 + 13,500 + 65,000 + 81,700 = 202,200
Northern Virginia Campaign casualties ~17,000
Remaining: 185,000 PFD.
With McClellan's approx. strength at Antietam at about 87,000 PFD, it should be clear that the forces left behind to defend Washington were enormous and may well have been larger than McClellan's field army. (Sanity checking confirms this, as there were two entire corps - 3rd and 11th, and 3rd was a really big one - plus the Washington Defences themselves which in late October were about 55,000 strong.)
In 1864, on the other hand, the Washington Defences were drawn down to about 20,000 men PFD (rough number, I've seen smaller). This had an enormous effect on the size of field army the Union could support; you'll also note it's less than the amount the corps commanders considered required...